When I run MTTs, there is me who handles cash and keeps tally, and one and only one designated helper who hands out chips, from the chip case that is closed and latched (not locked, but you can hear the latches snapping open) and the case is on a table at the edge of the room where no one needs to be unless they're getting chips. If one of us is in a hand (or getting beer), the other can take the cash or pass out the chips. If we're both engaged (in a hand, in bathroom, can't find the bottle opener), rebuy dude will have to wait the 45 seconds to get his chips.
In OP's case, I can't see how you can void the results, since you have no idea who did what. I know this won't be much consolation to most of your players, but the fact is, even a 10K bump to someone's stack doesn't have massive ICM implications. Here's my bored-at-work math on icmpoker.com, came up with this:
http://www.icmpoker.com/icmcalculator/#RVCy
For those who don't want to click, I asumed 5 ITM, max set up in this icm calc is 15 players so I gave them all 13333 chips, and one guy 14333. (This was based on 23 entries and 17 rebuys, for 240000 chips, or 13333 per person when down to 18 runners, when the stolen chips were introduced. The increase in prize equity for the thief went up just 0.4%, not nearly enough to void the results imo.)